Why is it necessary to have an earth wire installed in a power circuit, but not in a lighting circuit?

The appliances connected to the power circuit like air conditioner, geyser, washing machine, etc. consume heavy current. If due to some reason such as short circuiting, an excessive current flows through the power circuit, not only the appliance will get damaged but due to the excessive heat produced by such high current, the wires may get overheated causing a fire. If the earth wire is installed, it conducts the excessive current to the earth thus avoiding the fire.
The current carrying capacity of lighting circuit is low (less than 5A). In case of a short circuit, the chances of fire due to overheating of wires are little. Hence, generally earth wire is not installed in a lighting circuit.